New capability indices for measuring the performance of a multidimensional machining process

Engineering tolerance plays an important role in the process capability analysis for determining whether a manufacturing process is capable of making good quality products. In contrast with the engineering tolerance region in a multivariate manufacturing process, the multidimensional machining process or the nano-cutting process has a special engineering tolerance called the positional tolerance. Positional tolerance is a special type of geometric dimensioning and tolerancing which describes the tolerance region between the actual location of machining results and the target location. In the past few years, several capability indices have been developed for measuring the performance of a multidimensional machining process under the assumption that the variances of machining results on different directions are equal. However, this assumption may not be true in most practical situations. In this paper, we propose three novel capability indices for measuring the performance of a multidimensional machining process under the assumption that the variances of machining results on different directions may not be equal. The statistical properties of the point estimators and their confidence intervals for the new capability indices are derived. Both the simulation results and numerical examples show that the new capability indices outperform the predecessors.